At some level, every Calvinist who is not hyper embraces a paradox (you can call it tension, antinomy, aporia, really deep mystery, or whatever you like, but I prefer "paradox"). This is properly true of every Christian, but it is especially true of Biblical Calvinists. Our theology generates paradox, whether it's the apparent duality of divine wills, multiple senses of God's love and hatred for fallen humanity, or the compatibility of deterministic divine sovereignty and real human choice/freedom/responsibility. Calvinism without the essential balance of Biblically-derived paradox is in danger of going the way of Herman Hoeksema and the PRC. Characteristically, hyper-Calvinists eschew paradoxes in every possible way. Arminians, for their part, also seem reluctant to embrace paradoxes. Some take great delight in calling Calvinistic paradoxes "contradictions," ignoring the fact that these are unavoidable if we take divine revelation and historic/orthodox Christianity at face value.
THEOparadox is essentially a call for Calvinists (and others) to do two things:
1. Go whole hog and embrace every Biblically justified paradox, refusing to exegetically "adjust" any verse or passage of Scripture that might create a seeming contradiction in Systematic Theology.
2. Be rigorous in trying to understand, explain and evaluate possible resolutions to these paradoxes, but accept the fact that we can ultimately have no greater certainty than the very words of Scripture afford us.
It seems that many Calvinists don't want to follow through with their paradoxes, perhaps afraid they will end up in the murky slough of Neo-orthodoxy, or that embracing a Biblical "both/and" scenario somehow amounts to a denial of dearly held truth.
Whatever it is that drives some Calvinists to twist texts to their own liking, it is not a helpful thing. This bad habit leaves the door wide open for Arminians and others to criticize our theology on Biblical grounds. On the other hand, if we are copiously Scriptural in our affirmations and they criticize our position as "contradictory," they are really accusing Scripture of contradiction and leaving our paradoxes unscathed. Non-Calvinist Christians will find no holes in the fortress of Biblical Calvinism, except where our exegesis is unsound. That can be fixed. And of course they will find a gaping hole right in the center of our fortress: the open door of invitation to join us in believing ALL the Word of God (whether we like it or not, and whether we can explain it or not).
Someone will respond, "But that kind of thinking will destroy Systematic Theology!" This is only true if our Systematic Theology does not include a robust theory of knowledge that carefully balances the perspicuity of Scripture, the incomprehensibility of God, and the Creator/creature distinction.
Accepting Biblical paradox does not harm Systematic Theology; it enhances it. A well-developed Systematic Theology is essential and useful, but Biblical and Exegetical Theology are supreme. You can't have an accurate Systematic Theology if you don't have an in-depth knowledge of the texts themselves. To the extent that any system rejects even one tiny drop of the Bible, it reduces its own validity as a Christian system and partially cripples itself. Let's rather have a system that is hard to explain - yet Biblical to the core - than a system that explains itself by reducing the Word of God to man-made concepts.